Statistics: Assessing T-tests

Assessing T-tests To clearly identify what a t-test accomplishes in descriptive statistics it is imperative to understand what a t-test represents. A “t-test is a parametric statistical test for comparing the means of two independent samples” (Plichta & Kelvin, 2013, p. 464). Gosset developed the t-test for use in quality control at the Guinness Brewery and published his works under the pen name “Student” (Plichta & Kelvin, 2013). T-tests use assumptions related to the underlying variable of study, where it is assumed that the underlying variable is distributed normally (Fagerland, 2012, p. 76). In essence, the t-test examines differences between two groups on a variable of interest. Research Study Review

Bradley (2012), proposed to study the effects of nurse practitioners (NP’s) utilizing a skin cancer screening tool along with receiving further education on skin cancer assessment and diagnosis. The study was predicated on the Health Promotion Model (HPM), which was selected based on it relevance to the practice of NP’s and their duty to promote healthy behaviors (Bradley, 2012). “Evidence-based research showcased within the HPM can aid NPs in making practical recommendations to reduce skin cancer risk, specifically melanoma” (Bradley, 2012, p. 83). Study participants (NP’s) were provided with training and educational programs to increase their knowledge and subsequent assessment skills and documentation of physical skin assessments for patients. “The HPM was used in this study to examine the health status and health promotion behaviors of young adults with respect to screening for melanoma” (Bradley, 2012, p. 83). The study was conducted in two phases where “phase one utilized a quasi experimental design to examine characteristics of a single sample of NPs exploring the aspects of skin cancer screening phenomena among them in a single college health center setting” (Bradley, 2012, p. 83). NP’s were given a pre and post test to ascertain their cognitive processes and the changes in the ability to document properly based on the education they received (Bradley, 2012). “In quasi-experiments, the researcher does not have the ability to randomly assign the participants or ensure that the sample selected is as homogeneous as desirable” (Levy & Ellis, 2011, p. 155). NP’s attitudes were also evaluated after receiving the educational component to determine if attitude changes were elicited (Bradley, 2012). The study revealed an increase of correct documentation of skin cancer screening and education related to skin cancer (Bradley, 2012). Study Variables and Statistics

The study utilized a convenience sample of six certified NP’s who ranged in age from 40-64 (Bradley, 2012). Convenience sampling chooses samples that are readily available, this type of sampling can possess bias due to a lack of a statistical method of choosing the sample (DiCalogero, n.d.). The NP’s were given a Didactic skin cancer pre and post test, which consisted of 16 questions using a multiple choice format used to evaluate cancer knowledge and recognition (Bradley, 2012). “Test-retest reliability was r = .90, no alpha was given” (Bradley, 2012, p. 84). A program evaluation questionnaire using a Likert Scale was given following the post test to assess the NP’s attitudes, knowledge and perceptions related to relaying the skin cancer data and future participation in skin cancer screening for the public using a five point scale (Bradley, 2012). NP’s were also asked to use the screening tool for documentation via a pictorial display to document lesions and note patient education given (Bradley, 2012). Data collection transpired over a 30-day period. “Prior to the education, 30 randomly selected de-identified charts were retrospectively reviewed for skin cancer screening documentation” (Bradley, 2012, p. 85). At the conclusion of the study 22 additional charts were audited to note if improvement in the skin...

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...The T-Test
Page 1 of 4
Home » Analysis » Inferential Statistics »
The T-Test
The t-test assesses whether the means of two groups are statistically different from
each other. This analysis is appropriate whenever you want to compare the means of
two groups, and especially appropriate as the analysis for the posttest-only two-group
randomized experimental design.
Figure 1. Idealized distributions for treated and comparison group posttest values.
Figure 1 shows the distributions for the treated (blue) and control (green) groups in a
study. Actually, the figure shows the idealized distribution -- the actual distribution
would usually be depicted with a histogram or bar graph. The figure indicates where
the control and treatment group means are located. The question the t-test addresses
is whether the means are statistically different.
What does it mean to say that the averages for two groups are statistically different?
Consider the three situations shown in Figure 2. The first thing to notice about the
three situations is that the difference between the means is the same in all three But, you
three.
should also notice that the three situations don't look the same -- they tell very
different stories. The top example shows a case with moderate variability of scores
within each group. The second situation shows the high...

... The T-TEST
1.0 INTRODUCTION
The t-test was developed by W. S. Gossett, a statistician employed at the Guinness brewery. However, because the brewery did not allow employees to publish their research, Gossett's work on the t-test appears under the name "Student". The t-test is sometimes referred to as "Student's t-test." Gossett was a chemist and was responsible for developing procedures for ensuring the similarity of batches of Guinness. The t-test was developed as a way of measuring how closely the yeast content of a particular batch of beer corresponded to the brewery's standard.
And the same statistical methodology that compares a particular batch of beer to a standard can be used to compare how different any two batches are from each other. The test can be used to compare the yeast content of two kegs of beer brewed at separate times. Extending this into the realm of social phenomena, this methodology was used to address questions such as whether SAT preparation courses improve test scores or not and one of the advantages of the t-test is that it can be applied to a relatively small number of cases. It was specifically designed to evaluate statistical differences for samples of 30 or less.
2.0 DEFINITION OF T-TEST
A...

...of 1000 flights and proportions of three routes in the sample. He divides them into different sub-groups such as satisfaction, refreshments and departure time and then selects proportionally to highlight specific subgroup within the population. The reasons why Mr Kwok used this sampling method are that the cost per observation in the survey may be reduced and it also enables to increase the accuracy at a given cost.
TABLE 1: Data Summaries of Three Routes
Route 1
Route 2
Route 3
Normal(88.532,5.07943)
Normal(97.1033,5.04488)
Normal(107.15,5.15367)
Summary Statistics
Mean
88.532
Std Dev
5.0794269
Std Err Mean
0.2271589
Upper 95% Mean
88.978306
Lower 95% Mean
88.085694
N
500
Sum
44266
Summary Statistics
Mean
97.103333
Std Dev
5.0448811
Std Err Mean
0.2912663
Upper 95% Mean
97.676525
Lower 95% Mean
96.530142
N
300
Sum
29131
Summary Statistics
Mean
107.15
Std Dev
5.1536687
Std Err Mean
0.3644194
Upper 95% Mean
107.86862
Lower 95% Mean
106.43138
N
200
Sum
21430
From the table above, the total number of passengers for route 1 is 44,266, route 2 is 29,131 and route 3 is 21,430 and the total numbers of passengers for 3 routes are 94,827.
Although route 1 has the highest number of passengers and flights but it has the lowest means of passengers among the 3 routes. From...

...The T-Distribution and T-Test
“In probability and statistics, Student's t-distribution (or simply the t-distribution) is a continuous probability distribution that arises when estimating the mean of a normally distributed population in situations where the sample size is small” (Narasimhan , 1996). Similar to the normal distribution, the t-distribution is symmetric and bell-shaped, but has heavier tails, meaning that it is more likely to produce values far from its mean. This makes the t-distribution useful for understanding statistical behaviors of random quantities. It plays a role in a number of widely-used statistical analyses, including the Student's t-test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis.
Statistical significance is “measuring the likelihood that an event occurs by chance” (Statistical Assessment Service, 2000). In statistics, a result is called statistically significant if it is unlikely to have occurred at random. The amount of evidence required to accept that an event is unlikely to have arisen by chance is known as the significance level or p-value: “the p-value measures consistency by calculating the probability of...

...Two-Sample t-Tests
Connie Tyrone
Walden University
August 24, 2013
Two Sample t-Tests
With this assignment, we are told about Martha. Martha wants to see if her relaxing technique which involves visualization will be able to assist people suffering with mild insomnia to fall asleep faster. She randomly selects 20 insomnia patients to participate in her research. She assigns 10 from the group to participate in visualization therapy and 10 from the group receives no treatment. Martha then keeps a record of how long it takes each participant to fall asleep. As follows:
No Treatment (X1) Treatment (X2)
22 19
18 17
27 24
20 21
23 27
26 21
27 23
22 18
24 19
22 22
Our assignment is to respond to the following questions regarding Martha’s research study and her data.
Should Martha use an independent-samples t-test or a related samples t-test? Explain your answer.
Martha should use an independent-samples t-test. The independent-samples t-test is “the parametric procedure used for significance testing of sample means from two independent samples” (Heiman, 2012, p. 122). In Martha’s case, she has chosen 20 patients in which half will receive visualization therapy and half will not.
What are the independent and dependent variables?
The independent variable in this...

...Elements of a Test of Hypothesis 1. Null Hypothesis (H0 ) - A statement about the values of population parameters which we accept until proven false. 2. Alternative or Research Hypothesis (Ha )- A statement that contradicts the null hypothesis. It represents researcher’s claim about the population parameters. This will be accepted only when data provides suﬃcient evidence to establish its truth. 3. TestStatistic - A sample statistic (often a formula) that is used to decide whether to reject H0 . 4. Rejection Region- It consists of all values of the teststatistic for which H0 is rejected. This rejection region is selected in such a way that the probability of rejecting true H0 is equal to α (a small number usually 0.05). The value of α is referred to as the level of signiﬁcance of the test. 5. Assumptions - Statements about the population(s) being sampled. 6. Calculation of the teststatistic and conclusion- Reject H0 if the calculated value of the teststatistic falls in the rejection region. Otherwise, do not reject H0 . 7. P-value or signiﬁcance probability is deﬁned as proportion of samples that would be unfavourable to H0 (assuming H0 is true) if the observed sample is considered unfavourable to H0 . If the p-value is smaller than α, then reject H0 . Remark: 1. If you ﬁx α = 0.05 for your test, then...